None of the ones you've listed are offensive or off limits. Even atheists naming their kids Abraham or Moses isn't unbearable or rude.

- Omri - not a favourite of mine, but not a problem to use. I like Oren (which is also Hebrew) more just as a name, or Uri.
- Judah - I might guess that a little Judah was Jewish but it's not a problem for him not to be, its just not common. And a non-Jewish Judah is less remarkable, to my ear, than a non-Jewish Yehuda, though most Christians I have met by this name family are just Jude. I happen to really, really like Judah/Yehuda for my own list.
- Asa - I like it, but happen to like Avi, Ari, or Amos more. Just saying aesthetically. Not a problem to use.
- Avi - I like this a lot, along with Avram.

We named our daughter Orly, which is hebrew and mostly only found in Israel. A lot of people think we speak hebrew when they hear the name, but we do not speak any hebrew....we just love the name.
Our boy name was (and will be if we have a boy next) is Avi and it is my all-time favorite name.